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Table 6 Rate of rejection of the Rasch model assumption with the Q1 test as a function of the rate of missing data per item (π), the value of the correlation coefficient ρ between the latent variable Θ and the propensity to have missing data ξ for each method for handling missing data (results for w = 0/w = 1) [*: values significantly different of 5%]

From: Imputation by the mean score should be avoided when validating a Patient Reported Outcomes questionnaire by a Rasch model in presence of informative missing data

  π= 10% π= 20% π= 30%
Method ρ= 0.0 ρ= -0.4 ρ= -0.9 ρ= 0.0 ρ= -0.4 ρ= -0.9 ρ= 0.0 ρ= -0.4 ρ= -0.9
PMS 5.2/6.5 5.2/6.6* 4.9/6.3* 5.7/9.2* 5.9/9.7* 6.2/8.1* 4.6/22.3* 6.3/17.6* 6.2/18.5*
PMS-R 5.6/5.2 6.0/5.6 4.0/4.7 3.9/8.0* 4.3/6.4 6.2/6.0 5.2/8.5* 5.9/8.3* 6.7*/8.2*
IMS 5.6/3.9 5.4/4.6 6.0/5.8 4.5/4.6 6.3/4.4 6.1/5.3 3.9/4.5 3.9/5.0 6.1/5.8
IMS-R 6.0/6.0 6.0/6.1 4.5/5.0 6.2/6.7* 4.4/5.7 4.9/5.1 4.7/7.4* 5.9/5.5 4.3/6.8
CIM 11.4*/9.7* 8.5*/9.3* 9.0*/8.2* 19.6*/19.5* 15.5*/18.5* 14.2*/19.1* 22.9*/29.0* 22.2*/28.8* 23.6*/32.7*
CIM-R 5.9/3.7 4.9/4.4 5.2/4.4 6.9*/4.4 6.9*/5.6 6.6*/4.5 6.9*/5.5 6.8/4.9 8.0*/6.3
ICS 49.6*/54.8* 51.5*/55.2* 51.7*/54.0* 85.0*/87.9* 86.0*/88.6* 85.0*/89.0* 94.1*/97.6* 93.7*/96.5* 95.6*/97.7*
LOG 33.0*/37.3* 34.9*/34.6* 35.8*/37.2* 64.2*/63.6* 63.2*/67.4* 61.5*/65.9* 65.5*/65.6* 63.2*/68.1* 60.4*/66.9*
LOG-R 10.6*/12.6* 13.1*/11.1* 11.9*/11.6* 19.1*/19.8* 19.5*/18.7* 17.7*/19.0* 22.2*/26.4* 24.5*/24.8* 22.6*/24.0*
MOK 16.1*/17.3* 17.9*/18.6* 19.2*/19.4* 42.2*/51.3* 44.3*/54.2* 49.4*/56.9* 58.5*/72.4* 60.2*/75.0* 67.8*/82.0*
RAS 21.8*/23.8* 22.8*/24.3* 21.5*/26.1* 61.2*/69.9* 63.9*/67.6* 64.2*/67.5* 80.6*/87.7* 83.3*/88.7* 81.0*/86.3*
RAS-R 4.7/4.9 5.9/5.3 6.2/6.2 6.0/6.2 6.9*/6.9* 7.3*/6.0 6.6*/6.6* 6.7*/16.9* 6.8*/5.7
RAI 21.9*/24.3* 22.9*/24.3* 22.6*/27.5* 17.8*/45.0* 19.6*/40.2* 18.3*/36.9* 10.1*/61.0* 14.1*/52.5* 15.4*/45.0*
WORST 6.8*/5.5 6.1/5.8* 5.1/3.2* 6.7*/6.9* 6.2/4.4 5.0/4.8 10.0*/6.9* 9.2*/5.8 8.0*/4.0
NOIMP 6.5/7.8* 7.5*/8.2* 6.9*/7.6* 9.2*/9.7* 11.0*/10.9* 10.2*/9.4* 13.3*/14.8* 13.8*/14.0* 9.6*/9.5*
LD 4.9/5.1 4.0/5.2 5.1/4.9 4.8/5.2 5.1/5.0 4.3/4.4 3.4*/3.3* 3.4*/4.5 3.3*/2.5*
FC 5.2/5.5 4.8/4.4 5.1/5.0 5.4/4.6 4.1/3.9 4.9/4.9 4.0/4.8 4.7/4.5 4.9/3.8*